% Style file for CS5311 "Theory of Computation" documents
% Charles Wallace
% These style settings are what I use to format the lecture notes and homework assignments.
% Feel free to use as much (or as little) of them as you like.

\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{latexsym}
\usepackage{fullpage,parskip,paralist}
\usepackage{amsmath,amsthm,amssymb}
\usepackage{graphicx}

\ifdefined\nosol
  \newcommand{\sol}[1]{}
  \newcommand{\soltitle}{}
\else
  \newcommand{\sol}[1]{{\bf Solution.}  #1}
  \newcommand{\soltitle}{: Solutions}
\fi

\newcommand{\thetitle}[1]{\title{#1\soltitle}}
\author{}
\date{CS5311, Theory of Computation}

% \ie, \eg: the abbreviations the way they are supposed to be written
\newcommand{\ie}{{\em i.e.,}}
\newcommand{\eg}{{\em e.g.,}}

% These set common formats for various kinds of names
% \prob{P}: name of problem/language P
\newcommand{\prob}[1]{\mbox{\bf #1}}
% \pprob{P}{M}: problem P restricted to machine class M
\newcommand{\pprob}[2]{\mbox{$\prob{#1}_{\prob{\tiny #2}}$}}
% \prog{M}: name of program/machine M
\newcommand{\prog}[1]{\mbox{\tt #1}}
% \enc{M}: string encoding of machine M
\newcommand{\enc}[1]{\mbox{[\prog{#1}]}}
% \lang{M}: language accepted by machine M
\newcommand{\lang}[1]{\mbox{\bf L(\prog{#1})}}

% definition environment (unnumbered)
\theoremstyle{definition}
\newtheorem*{definition}{Definition}
% numbered environments: theorem, proof, lemma, corollary, claim
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{corollary}{Corollary}
\newtheorem{claim}{Claim}

% Proof opening statement
\newcommand{\prf}{{\em Proof.}}
\newcommand{\prfout}{{\em Proof outline.}}

% \code{L}{P}{I}{C}: Turing Machine code (as a box containing formatted text)
% L: horizontal length of box
% P: name of program
% I: names of inputs
% C: program code
\newcommand{\code}[4]{\fbox{\parbox{#1}
{\prog{#2}\hfill (Input: #3)
\begin{enumerate}
#4
\end{enumerate}}}}

% some common problems
\newcommand{\atm}{\pprob{A}{TM}}
\newcommand{\etm}{\pprob{E}{TM}}
\newcommand{\alltm}{\pprob{All}{TM}}
\newcommand{\acfl}{\pprob{A}{CFL}}
\newcommand{\allcfl}{\pprob{All}{CFL}}
\newcommand{\areg}{\pprob{A}{RL}}
\newcommand{\allreg}{\pprob{All}{RL}}
\newcommand{\anfa}{\pprob{A}{NFA}}
\newcommand{\adfa}{\pprob{A}{DFA}}

% \bigo{T}: big-O of term T
\newcommand{\bigo}[1]{\mbox{O$(#1)$}}
% \expbigo{T}: 2^(big-O of term T)
\newcommand{\expbigo}[1]{\mbox{$2^{\mbox{O$(#1)$}}$}}
% \bigom{T}: big-Omega of term T
\newcommand{\bigom}[1]{\mbox{$\Omega(#1)$}}
% time/space complexity terms
\newcommand{\TIME}[1]{\mbox{TIME$(#1)$}}
\newcommand{\NTIME}[1]{\mbox{NTIME$(#1)$}}
\newcommand{\SPACE}[1]{\mbox{SPACE$(#1)$}}
\newcommand{\NSPACE}[1]{\mbox{NSPACE$(#1)$}}
% some common complexity classes
\newcommand{\PTIME}{\mbox{P}}
\newcommand{\NPTIME}{\mbox{NP}}
\newcommand{\EXPTIME}{\mbox{EXPTIME}}
\newcommand{\PSPACE}{\mbox{PSPACE}}
\newcommand{\NPSPACE}{\mbox{NPSPACE}}
\newcommand{\LSPACE}{\mbox{L}}
\newcommand{\NLSPACE}{\mbox{NL}}
\newcommand{\coNLSPACE}{\mbox{coNL}}
\newcommand{\NC}{\mbox{NC}}
\newcommand{\NPcomplete}{\NPTIME-complete}

% \polyreduce{P}{Q} polynomial-time reduction relation
\newcommand{\polyreduce}[2]{$\prob{#1}\leq_{\mbox{\small P}}\prob{#2}$}
% \logreduce{P}{Q}: log-space reduction relation
\newcommand{\logreduce}[2]{$\prob{#1}\leq_{\mbox{\small L}}\prob{#2}$}

\newcommand{\gad}{\mathbf{Gadget}}
\newcommand{\domino}[2]
{\begin{tabular}{|l|} \hline $#1$\\ \hline $#2$ \\ \hline \end{tabular}}